Finding an Equation through Integrals

The acceleration of a certain rocket is given by ax = bt, where b is a positive constant.

(a) Find the position function x(t) if x = x0 and v0 at t = 0. (Use x_0 for x0, v_0 for v0, b, and t as necessary.)
x(t) =

2. Relevant equations

(Hint given): The velocity function is the time integral of the acceleration function. The position function is the time integral of the velocity function. The two integration constants can be determined by applying the given initial conditions when the time is equal to zero.